題目?jī)?nèi)容

If a machine can save only 3 significant digits, the float numbers 12300 and 12358.9 are considered equal since they are both saved as 0.123×10? with simple chopping. Now given the number of significant digits on a machine and two float numbers, you are supposed to tell if they are treated equal in that machine.

Input Specification:

Each input file contains one test case which gives three numbers?, ?and? , where?(＜100) is the number of significant digits, and ?and ?are the two float numbers to be compared. Each float number is non-negative, no greater than 101??, and that its total digit number is less than 100.

Output Specification:

For each test case, print in a line YES if the two numbers are treated equal, and then the number in the standard form 0.d[1]...d[N]*10^k (d[1]>0 unless the number is 0); or NO if they are not treated equal, and then the two numbers in their standard form. All the terms must be separated by a space, with no extra space at the end of a line.

Note: Simple chopping is assumed without rounding.

Sample Input 1:

Sample Output 1:

Sample Input 2:

Sample Output 2:

題目要點(diǎn)

本題 25 分，是一道比較復(fù)雜的模擬題，既要考慮一些邊界情況又要考慮浮點(diǎn)數(shù)帶來的精度損失，因此處理起來異常棘手。

如果使用Python解這道題，強(qiáng)烈建議使用下面代碼中標(biāo)準(zhǔn)庫的 decimal 模塊。因?yàn)轭}設(shè)中已知精確度范圍在100以內(nèi)，如果是小于1的小數(shù)，那么可能會(huì)精確到小數(shù)點(diǎn)百位，對(duì)于浮點(diǎn)數(shù)來說極易失去精度。如果直接使用輸入的字符串類型數(shù)據(jù)分析，也會(huì)遇到麻煩。比如，輸入數(shù)據(jù)可能是如0003.120這樣有前導(dǎo)零的不規(guī)范數(shù)字，還要先將不需要的零去掉。

經(jīng)過測(cè)試，測(cè)試點(diǎn)3、5的數(shù)據(jù)就是需要嚴(yán)格精度的。因此，在做這道題時(shí)會(huì)出現(xiàn)一個(gè)詭異的情況，在通過網(wǎng)上收集的許多測(cè)試點(diǎn)后仍然無法完全通過PTA的測(cè)試。所以，使用 decimal 模塊以定點(diǎn)數(shù)存儲(chǔ)數(shù)據(jù)，并充分利用模塊提供的一些方法可以極大地提高效率，直接針對(duì)問題的核心，避免陷入處理細(xì)枝末節(jié)的窘境。

源代碼

額外測(cè)試點(diǎn)

本題有許多邊界情況需要考慮，這里提供一些測(cè)試點(diǎn)以供參考。